Why Dividing by Zero Makes a Mechanical Calculator Go Berserk

Dividing by zero is complicated and we all know it's something you can't and shouldn't do. The simple—but still not perfect—explanation is that if you divide something by zero, the answer approaches infinity. And if you try it on a mechanical calculator, you're likely to get an illustration of why this happens as the calculator itself screams in robot agony.

Watch here as a certified mathematician (we can only assume) attempts to divide by zero on a mechanical calculator called the Facit ESA-01. And then watch the Facit ESA-01 completely lose its dang mind.

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Amusing, no doubt, but it's also a great little illustration of how mechanical computers work. These machines use a series of gears and cogs of different sizes to twist each other while the differential ratio between gears helps track the actual math. This video from 1953 explains it far better than I ever could, but here is how it looks when you multiple one by two with gears:

When a mechanical calculator divides, it uses a similar mechanical process, mostly likely one that's actually based on subtraction. As Numberphile explains in a fantastic episode about division by zero, division is basically just sequential subtraction. Twenty divided by four, for instance is just:

20 - 4 = 16

16 - 4 = 12

12 - 4 = 8

8 - 4 = 4

4- 4 = 0

Five steps to get to zero, so the answer is five. Simple!

Of course if you use the same process while dividing by zero, everything explodes because the sequence for 20 divided by zero is:

20 - 0 = 20

20 - 0 = 20

20 - 0 = 20

20 - 0 = 20

20 - 0 = 20

And on and on and oh no oh no oh no oh no.

Without a deep look inside this Facit ESA-01, it's hard to tell if this is exactly what's happening, or if there's more, mechanical nuance to the situation, but you can be sure that the underlying cause for the freakout is that the poor machine is trying to hammer out an infinite sequence of commands one by one by one.

A computer will always do exactly what you tell it to do, even if that will take literally forever.